This paper deals with the question of the existence of entropy solutions for the problem− div(a(x, u, ∇u) + φ(u)) + g(x, u, ∇u) = µ posed in an open bounded subset Ω of R^N with the homogeneous Neumann boundary condition (a(x, u, ∇u) + φ(u)) · η = 0. The functional setting involves Lebesgue and Sobolev spaces with variable exponent

Nonlinear elliptic problem, variable exponents, entropy solution, Neumannboundary conditions, Radon measure